(α,β)-Ricci-Yamabe Solitons with Potential Kuiper-Nash Vector Field
- 1Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, I. R. Iran
- 2Department of Mathematics, Payame Noor University, Tehran, I. R. Iran
- 3Department of Mathematics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, I. R. Iran
Abstract
This study focuses on identifying conditions that allow an n-dimensional compact Riemannian manifold (Mn, g) to support a vector field ξ along with smooth functions α and λ, forming an (α,β)-Ricci--Yamabe soliton structure. Our construction relies on embedding (Mn, g) isometrically into the Euclidean space (ℝm, g) following the method of Kuiper and Nash, where ξ is defined as the tangential component of a fixed unit vector in ℝm, hereafter called the Kuiper-Nash vector. Let r denote the scalar curvature of (Mn, g), we establish that whenever the integral of ξ(r) satisfies a specific lower bound dependent on a constant λ, the tuple (Mn, g, β r, ξ, λ) forms a valid (α,β)-Ricci-Yamabe soliton, which we term a Kuiper-Nash (α,β)-Ricci-Yamabe soliton. We examine conditions under which the soliton becomes trivial, presenting a characterization that directly relates this behavior to the scalar curvature r.Finally, an explicit characterization is derived for a compact, n-dimensional trivial Kuiper-Nash (α,β)-Ricci-Yamabe soliton, expressed in terms of an upper bound on the integral of (div ξ)2 that incorporates r.
Related
- Traversable wormhole de-singularization: almost η-Ricci–Yamabe solitons in static spherically symmetric imperfect fluid spacetimes
- Hyperbolic-Type Solitons on Ricci Pseudo-Symmetric Riemannian Concircular Structure Manifolds
- Size, atmospheric, and ring constraints on the large Kuiper belt object (55565) Aya from a stellar occultation
- Orientation of the spin axes of large Kuiper belt bodies as an indicator of the mechanism of their origin
- Orientation of the spin axes of large Kuiper belt bodies as an indicator of the mechanism of their origin
BibTeX
@article{azami2026αβricciyamabe,
title = {{$(\alpha,\beta)$-Ricci-Yamabe Solitons with Potential Kuiper-Nash Vector Field}},
author = {Shahroud azami and Mehdi Jafari and Mosayeb Zohrehvand},
journal = {Mathematics Interdisciplinary Research},
year = {2026},
month = oct,
doi = {10.22052/mir.2026.258097.1561},
url = {https://doi.org/10.22052/mir.2026.258097.1561},
note = {CC BY},
}
RIS
TY - JOUR
TI - (α,β)-Ricci-Yamabe Solitons with Potential Kuiper-Nash Vector Field
AU - Shahroud azami
AU - Mehdi Jafari
AU - Mosayeb Zohrehvand
PY - 2026
DA - 2026/10/30
JO - Mathematics Interdisciplinary Research
DO - 10.22052/mir.2026.258097.1561
UR - https://doi.org/10.22052/mir.2026.258097.1561
AB - This study focuses on identifying conditions that allow an n-dimensional compact Riemannian manifold (M^n, g) to support a vector field ξ along with smooth functions α and λ, forming an (α,β)-Ricci--Yamabe soliton structure. Our construction relies on embedding (M^n, g) isometrically into the Euclidean space (ℝ^m, g) following the method of Kuiper and Nash, where ξ is defined as the tangential component of a fixed unit vector in ℝ^m, hereafter called the Kuiper-Nash vector. Let r denote the scalar curvature of (M^n, g), we establish that whenever the integral of ξ(r) satisfies a specific lower bound dependent on a constant λ, the tuple (M^n, g, β r, ξ, λ) forms a valid (α,β)-Ricci-Yamabe soliton, which we term a Kuiper-Nash (α,β)-Ricci-Yamabe soliton. We examine conditions under which the soliton becomes trivial, presenting a characterization that directly relates this behavior to the scalar curvature r.Finally, an explicit characterization is derived for a compact, n-dimensional trivial Kuiper-Nash (α,β)-Ricci-Yamabe soliton, expressed in terms of an upper bound on the integral of (div ξ)^2 that incorporates r.
SN - 2476-4965
ER -